Adjacent well separation factor algorithm considering the influence of error ellipsoid envelope

To achieve efficient hydrocarbon resource development, cluster wells and infill wells are increasingly utilized in directional drilling projects. During the design and construction phases of such projects, the separation factor calculation serves as a critical step for collision avoidance management. Although various methods for computing separation factors have been developed, most existing approaches—including the SPE-WPTS-recommended method—consider only the error ellipsoids at designated reference well points and the closest points of offset wells, neglecting the error ellipsoid envelope. This oversight likely leads to an underestimation of collision risks. Building on the SPE-WPTS algorithm, this study proposes a novel separation factor calculation method that incorporates the error ellipsoid envelope, termed the ‌error envelope separation factor‌. The method approximates segments of wellbore trajectories as elliptical cylinders and constructs parametric equations using analytical geometry. Distance uncertainty is quantified via projections of these cylinders along the direction from a specified point on the reference well to the nearest point on the offset well. Example calculations show that when the reference well is parallel to the offset well, the error envelope separation coefficient has the same calculation result as the separation coefficient recommended by SPE-WPTS. As the degree of non-parallelism between the reference and offset wells increases, the difference between the error envelope separation coefficient and the separation coefficient recommended by SPE-WPTS becomes larger and larger. At this time, it is more scientific to apply the error envelope separation factor. The main contribution of this study is that the proposed method of calculating the error envelope separation factor improves the accuracy of wellbore collision risk prediction, and the proposed algorithm for the uncertainty of the distance between two wellbore points is also important for well spacing optimization.